answer key • lesson 10: add...

1 TG • Grade 5 • Unit 2 • Lesson 10 • Answer Key

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Student Activity Book

Find Fraction Sums 1 (SAB pp. 95–97) Questions 1–12

1. blue; 1–8 � 1–4 � 1–4 � 5–8 ; 1–8 � 2–8 � 2–8 � 5–82. aqua; 1–2 � 1–6 � 4–6 ; 3–6 � 1–6 � 4–63. aqua; 1–3 � 1–6 � 3–6 ; 2–6 � 1–6 � 3–64. black; 1–4 � 1–4 � 1–3 � 10–12 ; 3–12 � 3–12 � 4–12 � 10–12

Note: students may see that 2–4 is the same as 1–2and then reason that they can trade for sixths(orange pieces) 3–6 � 2–6 � 5–6 . This is a correctsolution, even though it does not comply withour rule that trades only be made when the newpieces cover the individual pieces exactly.

5. purple; 3–5 � 1–10 � 7–10 ; 6–10 � 1–10 � 7–106. black; 1–4 � 5–12 � 8–12 ; 3–12 � 5–12 � 8–127. black; 1–12 � 1–6 � 1–3 � 1–6 � 9–12 ; 1–12 � 2–12 � 4–12 � 2–12 � 9–128. black; 1–2 � 1–12 � 1–4 � 1–12 � 11–12 ; 6–12 � 1–12 � 3–12 � 1–12 � 11–129. black; 1–4 � 1–6 � 5–12; 3–12 � 2–12 � 5–12

10. black; 1–4 � 1–3 � 1–3 � 1–12 � 12–12or 1;3–12 � 4–12 � 4–12 � 1–12 � 12–12 or 1; 3–12 � 8–12 � 1–12 � 12–12 or 1

11. 1–6 � 2–6 � 3–612. 3–12 � 2–12 � 5–12

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Add Fractions SAB • Grade 5 • Unit 2 • Lesson 10 95

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Find Fraction Sums 1Fraction sums are shown with fraction circles in the first column of the chartbelow. Use fraction circle pieces to show the problem. Find the sum usingpieces of only one color. Draw a picture to show how you solved it in thesecond column. Write the color you used in the blank. Write two numbersentences for the sum in the third column. The first row is an example.

Using One Color Number Sentences Fraction Sum

Example Color:

1. Color:

2. Color:

3. Color:

4. Color:

Black

Y OR

B Y

Y

PK

A

A OR

Y Y

OR

1–41–3

7—12+ =

3—124—12

7—12+ =

P

P

Student Activity Book - Page 95

Using One Color Number Sentences Fraction Sum

Color:

6.

5.

Color:

7. Color:

8. Color:

9. Color:

10. Color:

P

PK

BK

BK

Y

G

G

G

Y

BK

BK BK BK

BK

BK

OR

A

A

Y

A

OR

OR

Y

BK

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96 SAB • Grade 5 • Unit 2 • Lesson 10

Add Fractions


Julia solved Question 2 this way.

11. Use Julia’s way to solve Question 3.

12. Use Julia’s way to help Romesh solve Question 9.

Julia

If I can rename as sixths, they will be easier to add.

C

1—2?—6

1 � ?————2 � ?

1—6�

=

3—64—6

1—6� =

3—61 � 3————2 � 3 = PK

A

— = —

1—2

3�1 3

=

� 6—1

?�2 ———— ?�1 6—?

2—1

siebe ea

s sixthsaan rIf I c

PK

A d.do ar tsie

lily w, thes sixthse enaman r 2—

1

= 3�2 ———— 6—

=� 6—1

6—4

6—3

ailuJ

4

1

1—6

1—6

———61 � ——————3 �

1—3�

�

=

=

OR

A

———6

— = —

———

=

� 3—1

3 ——————�16———

6—1

=�

� 3 6

6—1 ———6———

OR

A

4

1

Y

Romesh

I

Can I rename them as sixths? No. Fourths? No. Twelfths? Yes!

1

?—61 � ?————4 � ? = NO ?—4

1 � ?————6 � ? = NO

3

1—41—6�

A

———121 � ———————4 � = ———12

1 � ———————6 � =

� =———12———12 ———

Can I r

—

= ?�1

� 6—1

4—1

= ?�1 ?NO?

NO?

Y

shemRo? YthsfwelTthsruo F.oN

s sixthsthem aenamCan I r

Y

= ?�4 ———— —

!se Y .o? Nths? s sixths

e enam

A

� 4 ———————� 1

= ?�6 ———— 4—NO6—

———12——— 12——— =�

� 6 ———————� 1=——————— 12———

NO4—

=——————— 12———

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Answer Key • Lesson 10: Add Fractions

TG • Grade 5 • Unit 2 • Lesson 10 • Answer Key 2


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yFind Fraction Sums 2 (SAB pp. 99–101) Questions 1–6

1. aqua; 1–3 � 1–3 � 1–2 � 7–6 ; 2–6 � 2–6 � 3–6 � 7–6 ; 7–6 � 11–62. black; 2–12 � 3–4 � 2–3 � 19–12; 2–12 � 9–12 � 8–12 = 19–12; 19–12 � 17–123. blue; 1–2 � 3–4 � 1–8 � 11–8 ; 4–8 � 6–8 � 1–8 � 11–8 ; 11–8 � 13–84. aqua; 1–3 � 1–2 � 3–6 � 1–3 � 10–6 ; 2–6 � 3–6 � 3–6 � 2–6 � 10–6 ;

10–6 � 14–65. 4–6 � 3–6 � 7–6 � 11–66. A. 4–8 � 7–8 � 11–8 � 13–8

B. 5–6 � 4–6 � 9–6 � 13–6 or 11–2C. 9–12 � 10–12 � 19–12 � 17–12

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Find Fraction Sums 2Fraction sums are shown with fraction circles in the first column of the chartbelow. Use fraction circle pieces to show the problem. Find the sum usingpieces of only one color. Draw a picture to show how you solved it and writetwo number sentences for the sum in the second column. Show and write thesum as a mixed number in the third column. The first row is an example.

Using One Color Shown As

Mixed Number Fraction Sum

Example Color:

Number Sentences: Number Sentences:


Color: Color: 1.

Purple Color: Purple

3—104–5

11—10+ =

3—108—10

11—10+ = 11—10

1—10= 1

P P G

G

G

G

P

OR

OR

PK


Julia solved 3—10 � 4—5 this way:

5. Solve Question 1 Julia’s way. Find equivalent fractions with commondenominators.

6. Use Julia’s way to solve the problems.

A. 1—2 � 7—8 = ? Number sentence:

B. 5—6 � 2—3 = ? Number sentence:

C. 3—4 � 10—12 = ? Number sentence:

8——103——10

8——1011——10

4 � 2—————5 � 2

=

=

11——10= 1�

—

Julia

If I can rename astenths, they will be easier to add.

G G

G

G

P

P

P

4—5

� 1=

=

=

2�5 ————— 2�4

10——1110——810——310——8

1 10——11d.do a trsieea

y w, thethsentenaman rIf I c

ailuJd.

l be ily ws 5enam 5 —e a4

P

P

P

G

G

G

G

3

Pk

Or

Or

2—31—2�

———62 � ———————3 � = ———6

1 � ———————2 � =

� =———6———6 ——— = ———

J

�12

6——— ———�

=� 3 ———————� 2

6———

———=———6——— =

=� 2 ———————� 1

6———

� 2—3—

Pk

Or

——— Or

Pk

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Add Fractions

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Using One ColorShown As

Mixed NumberFraction Sum

Color:



Color:Color:3.


Color:Color:4.

2.Color:

BPK

PK

OR

OR

Y Y

YBK

BK

Y Y

Y

OR

OR

A A

A


3 TG • Grade 5 • Unit 2 • Lesson 10 • Answer Key

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Fraction Problems (SAB pp. 103–104) HomeworkQuestions 1–5

1. A. 4–3 � 8–6B. 2–3 � 6–9C. 4–12 � 1–3D. 9–12 � 3–4E. 5–2 � 15–6F. 6–8 � 9–12G. Possible response: I found an equivalent

fraction for 6–8 by dividing both thenumerator and the denominator in half. Igot 3–4 . Then I found an equivalent fractionfor 3–4 with a denominator of 12 bymultiplying the numerator by 3. I got 9–12 .3–4 � 6–8 � 9–12 .

2.

3. A. 3–5 � 7–10 � 13–10 � 13–10 or 6–10 � 7–10 � 13–10 or 13–10B. Levi

4. 2–9 � 2–3 � 8–9 or 2–9 � 6–9 � 8–95. A. 1–4 � 1–2 � 2–8 � 8–8 or 1 or 2–8 � 4–8 � 2–8 � 8–8 or 1

B. EmilyC. Possible response: I know 1–4 � 1–2 and I know

2–8 � 1–2 , so since Emily ate 1–2 of thesandwich, she ate the most.

11——4

16——3

15——2

14——5

25——8

ImproperFraction

MixedNumber

Letter

3—421—35

1—274—52

1—83

P A R YT

Fraction Problems

1. Find the missing numerator or denominator.

A. B.

C. D.

E. F.

G. Explain how you solved Question 1F.

2. Change the improper fractions to mixed numbers. Then use the code to findthe mystery word.

Code

The mystery word is .

4—3 ———6= 2—3

6———=

4——121———= ———4

9——12=

———65——2

=

11——4

16——3

15——2

14——5

25——8

ImproperFraction

MixedNumber

Letter

1—27

MixedNumber

Letter

1—42 2—

35 24—5

1—83 3—

42 1—84 1—

35

E O R T Y P N A

———126——8

=

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Solve the problems about Mr. Moreno’s classroom party.

3. Carla ate 3�5 of her bag of popcorn and Levi ate 7�10 of his bag of popcorn.

A. How much popcorn did they eat altogether? Write a number sentence.

B. Who ate more popcorn?

4. Mr. Moreno ordered a jumbo pizza for the classroom party. 2�9 of the pizza hadgreen peppers, 2�3 of the pizza had mushrooms, and 6�12 of the pizza hadpepperoni. How much of the pizza had vegetables on it? Write a numbersentence.

5. There was a large submarine sandwich at the party, too. Miguel ate 1�4 of thesandwich, Emily ate 1�2 of the sandwich, and Roberto ate 2�8 of the sandwich.

A. How much of the sandwich did they eat altogether? Write a numbersentence.

B. Who ate the largest portion of the sandwich?

C. Show or tell how you solved Question 5B.

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